What is the $\ell_{2, 1}$ norm?
$l_{2,1}$ is a matrix norm, as stated in this paper. For a certain matrix $A \in \mathbb{R}^{r\times c}$, we have  $$||A||_{2,1} = \sum_{i=1}^r \sqrt{\sum_{j=1}^c A_{ij}^2}$$ 
You first apply $l_2$ norm along the columns to obtain a vector with r dimensions. Then, you apply $l_1$ norm to that vector to obtain a real number. You can generalize this notation to every norm $l_{p,q}$.